Wave packet analysis, time-dependent

Time dependent wave packet analysis of FOIST... 

In the time dependent wave packet analysis (21) the Schrodinger equation... 

Analysis of time-dependent wave packets in terms of scattering states - why and how... 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

In WP analysis the time evolution of an initial wavefunction (or wave-packet) is obtained by the solution of the appropriate time-dependent Schrbdinger equation. The initial wavefunction is determined by the conditions of the collision. The Schrbdinger equation is then integrated, which given the complexity of the potentials usually has to be performed numerically. Information about the crossections can be obtained from this technique and again canonical rate coefficients obtained by the above averaging procedure. 

The time-dependent theory of spectroscopy bridges this gap. This approach has received less attention than the traditional time-independent view of spectroscopy, but since 1980, it has been very successfully applied to the field of coordination chemistry.The intrinsic time dependence of external perturbations, for example oscillating laser fields used in electronic spectroscopy, is also expKdtly treated by modern computational methods such as time-dependent density functional theory, a promising approach to the efficient calculation of electronic spectra and exdted-state structures not based on adjustable parameters, as described in Chapter 2.40. In contrast, the time-dependent theory of spectroscopy outlined in the following often relies on parameters obtained by adjusting a calculated spectrum to the experimental data. It provides a unified approach for several spectroscopic techniques and leads to intuitive physical pictures often qualitatively related to classical dynamics. The concepts at its core, time-dependent wave functions (wave packets) and autocorrelation functions, can be measured with femtosecond (fs) techniques, which often illustrate concepts very similar to those presented in the following for the analysis of steady-state spectra. The time-dependent approach therefore unifies spectroscopic... 

To evaluate the product branching ratio for both the IBr and the HI molecules, we have carried out time-dependent wave packet (TDWP) analysis, where the Schrodinger equation... 

The understanding, interpretation and practical tools to approach the problem of resonances states in quantum chemistry and molecular physics are basically very well studied. Generally one has either (i) concentrated on the properties of the stationary time-independent scattering solution (ii) attempted to extract the Gamow wave by analytic continuation and/or (iii) considered the time-dependent problem via a suitably prepared reference function or wave-packet. In each case the analysis prompts different explanations, numerical techniques and understanding, see e.g. Ref. [15] for a review and more details. 

In our computational work, on which the following numerical analysis is based, the multiconfiguration time-dependent Hartree (MCTDH) method is used [18-20]. This method is, the only one at present, which can propagate the multidimensional wave packet and treat the multi-mode quantum dynamics of polyatomic systems with controllable accuracy up to 20-30 modes. 

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